One popular argument we often hear from investors that I speak with as part of my work at Mutiny Fund is “I’m a long-term investor. Short-term volatility or drawdowns don’t matter to us because I am happy to hold the assets for the long-term.”

I hear this particularly from people who have learned about investing a lot from the Warren Buffett/Jack Bogle camp as they often are quoted in soundbites to this effect. (though, I think their actual views are significantly more nuanced and sophisticated than the naive interpretation of that statement).

Benn Eifert, CIO of QVR, noted and articulated that these sorts of statements often belie a misunderstanding of how compound growth actually works and I’d like to explore that a bit.

Let’s start with a fun trivia question: You have two return streams (a return stream could be a stock, bond, particular trading strategy, etc.)

You know that both will average an annual return of 10%.

There is only one difference between the two return streams:

- Return Stream Low Volatility (LowVol) has an annualized volatility of 10%
- Return Stream High Volatility (HighVol) has an annualized volatility of 20%

What is the compounded annual growth rate (CAGR) of each? (don’t look down the page and cheat!)

- LowVol has a higher compounded annual growth rate (CAGR)
- HighVol has a higher compounded annual growth rate (CAGR)
- They have the same compounded annual growth rate (CAGR)

Got your answer?

The only difference is one goes up and down more than the other which doesn’t matter.

Or does it?

In a very unscientific survey of my Twitter followers, 42.4% of people thought they had the same long-term CAGR.

However, the long-term compound growth rates for LowVol will be 9.5% while the long-term compounded return of HighVol will be 8%.

**The more volatility in the return stream, the worse the long-term returns**. A 10% average annual return stream with 40% volatility will compound at only 2% per year. At 50% volatility, a return stream with a 10% average annual return will actually lose money over time!

This is not very intuitive, but once you work out an example, it makes sense.

As a simple example, let’s say you own a $1 million portfolio. Yay!

In Year 1, it suffers a 50% drawdown. Boo!

However, the next year, the market makes a breathtaking rally of 100%. Amazing!

Over that two-year period, your average annual return is 25%: (A -50% loss in year 1 + 100% Gain in year 2 divided by 2 years = 25% average annual return). However, what is the total portfolio value at the end of the second year?

Well, your $1 million declined to $500,000 in Year 1 (a loss of -50%) and then grew 100% from there to get back to exactly where you started: $1 million, a 0% compounded return.

As the saying goes, your 25% average annual return and two bucks will get you a cup of coffee. In the long run, the compounded return is all that matters. And the volatility of the return stream matters quite a lot to the compounded growth.^{1}

Despite the breathtaking rally, your wealth is not growing over that time period, merely recovering to where it started.

Let us call this the **Iron Law of Volatility Drag: the higher the volatility of a portfolio, the worse the long-term compound rate of growth of a portfolio, all else being equal.**

One of the big lessons from the Iron Law of Volatility Drag is that large drawdowns significantly impair long-term compounding of wealth.

Here’s one (toy) model for thinking about this:

If you had invested $100,000 in the S&P in August, 1989 would have finished with $1,935,000 in August, 2020. Not too shabby!

What happens if you take away some of the downside volatility and drawdowns?

Well, removing 10% of the largest losses means that the portfolio grows to $2,429,000. Removing just 10% of the losses increases the long-term wealth by over 25%!

Removing 20% of the largest losses increased it by $1.235mm to $3,170,000.

Removing the largest 30% of losses led to more than a doubling in the long-term wealth, a final value of $4,002,000, a difference of $2.067mm.

This example is purely illustrative and based on a toy model, but shows the Iron Law of Volatility Drag and it’s biggest consequence: large drawdowns and downside volatility dramatically impair the long-term, compounded growth rate of a portfolio.

To reduce drawdowns and more effectively compound wealth over the long term requires true diversification. I believe the easiest way to think about this is as categorizing assets as either offensive (risk-on) or defensive (risk-off).

The offensive bucket is most easily thought of as any long GDP asset, typically correlated to the S&P 500 and broad economic growth. These include: stocks, bonds, private equity, venture capital, and real estate. They are assets that perform well most of the time, but when they perform badly, they perform really badly as we’ve seen in prior crises such as 2008 or 2001.

In the defensive bucket would be anything that is short GDP, typically uncorrelated or negatively correlated to the S&P 500. Defensive assets include things like commodities, Gold, and long volatility/tail risk option strategies. They are assets that can struggle for longer periods of time, but they perform well at the time when the offense needs it the most, providing effective diversification across decades of market cycles.

Many of the same investors that say they don’t care about short-term volatility or drawdowns think that they are smarter in the long run: “I don’t want to invest in defensive assets because I am a long-term investor and defensive assets have poor long-term returns. I care about the long-term returns and I can tolerate the drawdowns.”

The Iron Law of Volatility Drag shows you need both offense and defense to minimize the volatility of the portfolio, but also to get the best long-term returns.

Let’s look at what happens when you add a little defense to an offense-only investment strategy.

For this example, consider a simple defensive strategy, buying put options on the S&P.^{2}

*If you’re familiar with options trading, skip down to the chart below, if not here’s a quick explanation:*

An option is a financial instrument that allows investors to buy and sell the right, but not the obligation (i.e. the “option”) to buy or sell an underlying asset at a specified time at a specified price.

**Call options**allow the holder to buy the asset at a specified time at a specified price. A call option generally benefits when the price of the underlying asset increases over time so it is a bet on the market going up.**Put options**allow the holder to sell the asset at a specified time at a specified price. A put option generally benefits if the price of the underlying asset will decrease so it is a bet on the market going down.

For example, if there is a stock currently trading at $100, you could buy a put option for the right to sell the asset at a specified time (say the end of next month) at a specified strike price (say $90).

Let’s say this option costs $1. So, you pay $1 up front for the right to sell the stock for $90 at the end of the coming month. If the price of the stock falls to $85 in that time period, you can buy the stock for $85 in the market and use your option contract to sell it for $90. Once you deduct the $1 you paid for the option, you pocket a $4 profit .

If the stock ends the month at any price higher than $90, then the option expires worthless and you lose the $1 you paid for the option.

In this example, your maximum potential loss over this time period is $11, the cost you paid for the option plus the $10 difference between the current price and the strike price of the option you bought.

A put option is conceptually similar to an insurance policy. When you buy health insurance, typically you pay the premium up front (~= the price of the option) then you are on the hook for the deductible (the difference between the strike price and current price). Beyond that, the insurance kicks in and covers any expenses. If you have a $5,000 premium and $10,000 deductible in a calendar year then your maximum loss is capped at $15,000 for that year. Even if you get hit by a bus and rack up a million dollars in medical bills, you’re only on the hook for $15,000.^{3}

The price of the option (in this case, $1) is equivalent to an insurance premium that you pay whether you use the insurance or not. If you own one share of the stock at $100 and you pay $1 for the put option with a $90 strike price then the $10 difference between the current price and the strike price is similar to your deductible. You can lose $10 “out of pocket” before the insurance kicks in. Buying this put option costs you something ($1), but you are guaranteeing that you can’t lose more than $11 over that time period, effectively capping your losses similar to how most insurance policies work.

Similar to buying insurance, put buying by itself is a long-term losing strategy. Over the long run, insurance companies are profitable so the total premiums paid in is more than the amount paid out. On average, policyholders lose. However, this doesn’t mean buying insurance is dumb!

As expected, the performance of our put buying strategy on the S&P doesn’t look very attractive. Over a nearly 20 year period, it has lost money.

Why would anyone invest in this defensive strategy that loses money over time when they could invest in something that makes money over time?

The popular understanding I most often hear is that it’s because these people are “scared” or “not thinking long-term.”

Eifert did some research adding this exact (money-losing) strategy to a 60% stock/40% bond portfolio with quarterly rebalancing between all three components.

The blue line is the 60% stock/40% bond portfolio and the orange line includes adding in the put buying strategy.

The portfolio which includes the money-losing defensive strategy has higher long-term returns.

How can adding a strategy which loses money over the long-term increase the portfolio returns? Because of the Iron Law of Volatility Drag.

Even though the defensive strategy loses money on average, it makes money at the times when the rest of the portfolio struggles. The outsized performance of the defensive during large market drawdowns allows a regularly rebalanced portfolio to buy risky assets in the periods immediately following those large market drawdowns.

It reduces the total volatility of the portfolio enough to compensate for the fact that it is a losing strategy as a stand-alone.

That’s why effective diversification including both offensive and defensive strategies can make such a big impact on long-term wealth.

I believe that the best portfolios are equal parts offense and defense. Defensive strategies like the put buying strategy tend to look worse as a standalone and so investors fail to incorporate them in their portfolios, even though they improve the overall performance of the portfolio.

By including equal parts offense and defense, an investor seeks to achieve the “free lunch” of diversification:

- They are seeking to maximize terminal wealth…
- while also minimizing drawdowns so that you can have confidence that their savings will be there when you need it.

Though these are the goals that most investors have for their wealth, few investors actually structure their portfolios to achieve them.

If your goal is to maximize your expected long-term wealth while also knowing you’ll be able to handle whatever life comes at you, you need both offensive and defensive assets in your portfolio.

*H/t and Image Credits to Benn Eifert.*

Last Updated on September 16, 2021 by Taylor Pearson

#### Footnotes

- Unnecessary but interesting (IMO at least) and slightly technical aside: For any given series of data, you can calculate either a
*geometric*average or an*arithmetic*average.The arithmetic average is what we are familiar with and what people mean when they say the word average (Or use =AVERAGE in Excel). It is where you add the values in the series together and divide by the number of values like I did here. When I say “annual average return,” I am referring to the arithmetic average.

Let’s take a simple example of a data series with two numbers: 1 and 2

The arithmetic average of 1 and 2 is 1.5: (1 + 2)/2=1.5

The geometric average is different. It is calculated by multiplying the two values together and taking the square root.

So the geometric average of 1 and 2 is: (2*1)=2. Then the square root of 2 is 1.41.

Critically,

*the geometric average will always be the same or lower than the arithmetic average*.The geometric average is often referred to in investing as the Compound Annual Growth Rate (CAGR). This matters in large part because the geometric average/CAGR is what people really care about. It is the “returns you can eat.” However, most financial media and pundits tend to talk about the arithmetic average which nearly always significantly overstates the arithmetic average.

So the next time you hear some talking head on the news or CNBC say something like “the average return of [insert whatever they are shilling] is 20% per year,” remember that they are an idiot and that the arithmetic average return is mostly meaningless and don’t pay attention to them.

Despite the breathtaking rally, your wealth is not growing over that time period, merely recovering to where it started.

- This example will use 1-year 30-delta puts, delta hedged and rolled quarterly.
- There are, of course, a gajillion clauses in practice that insurance companies use to try and avoid paying out claims, so this is simplified, but you get the point.